Synthetic aperture radar (SAR) as a method for ground imaging by using a single antenna or a sensor array has widely found attraction for remote sensing applications and reconnaissance tasks. Independent of the particular sensor but inherent to the SAR processing, moving objects in the observed scene are imaged at incorrect positions and can appear in a smeared fashion. For countering these disturbing artifacts a joint spatial-spectral processing is proposed and analyzed in this paper that allows to suppress echoes from moving targets in multi-channel stripmap SAR data while preserving the echoes of the fixed scene. Results obtained with experimental data from an airborne system show the potential and limitations for a practical application of the presented method.